Worksheet on Application of Factor Theorem

Practice the questions given in the worksheet on application of Factor Theorem.

1. Find the roots of the equation 6z$^{2}$ + 11z -10 = 0. Hence, factorize 6z$^{2}$ + 11z -10.

2. Find the roots of the equation 2m$^{2}$ - 3m - 6 = 0. Hence, factorize 2m$^{2}$ - 3m - 6 = 0

3. Find the roots of the equation p(p + 1) - 4 = 0. Hence, factorize 4 - p - p$^{2}$.

4. Find the quadratic equation whose roots are

(i) -3, 7

(ii) 2 + √3, 2 - √3

(iii) $\frac{1}{√3}$, - $\frac{1}{√3}$

5. Find the cubic equation whose roots are

(i) 1, 2, 3

(ii) -4, √3, -√3

(iii) $\frac{1}{2}$, $\frac{√5}{2}$, $\frac{-√5}{2}$

Answers for the worksheet on application of Factor Theorem are given below:

Answers:

1. $\frac{2}{3}$ , $\frac{-5}{2}$; (3z - 2)(2z + 5)

2. $\frac{3 + √57}{4}$, $\frac{3 - √57}{4}$; (2m - $\frac{3 + √57}{2}$)(m - $\frac{3 - √57}{4}$)

3. $\frac{-1 + √17}{2}$, $\frac{-1 - √17}{2}$; ($\frac{-1 + √17}{2}$ - p)( $\frac{1 + √17}{2}$ + p)

4. (i) y$^{2}$ - 4y -21 = 0

(ii) z$^{2}$ - 4z + 1 = 0

(iii) 3p$^{2}$ - 1 = 0

5. (i) z$^{3}$ - 6z$^{2}$ + 11z - 6

(ii) m$^{3}$ + 4m$^{2}$ - 3m - 12

(iii) 8k$^{3}$ - 4k$^{2}$ - 10k + 5 = 0

10th Grade Math

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